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Metamath Proof Explorer

Theorem rabbii

Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv . (Contributed by Peter Mazsa, 1-Nov-2019)

		Ref	Expression
	Hypothesis	rabbii.1	⊢ ( 𝜑 ↔ 𝜓 )
	Assertion	rabbii	⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } = { 𝑥 ∈ 𝐴 ∣ 𝜓 }

Proof

Step	Hyp	Ref	Expression
1		rabbii.1	⊢ ( 𝜑 ↔ 𝜓 )
2	1	a1i	⊢ ( 𝑥 ∈ 𝐴 → ( 𝜑 ↔ 𝜓 ) )
3	2	rabbiia	⊢ { 𝑥 ∈ 𝐴 ∣ 𝜑 } = { 𝑥 ∈ 𝐴 ∣ 𝜓 }